Page 206 - Ganit Kaushal

3 5 7 11
Ex. Arrange the fractions ,, , in ascending order.
4 9 18 12
Sol. The given fractions are unlike fractions with different numerators.
To compare them, we convert all to equivalent fractions with a common denominator.
Now, LCM (4, 9, 18, 12) = 2 × 2 × 3 × 3 = 36 2 4, 9, 12, 18
3 39 27 5 54 20 7 7 × 2 14 11 11 3 33 2 2, 9, 6, 9
×
×
×
So, = = , = = , = = , = = 3 1, 9, 3, 9
×
4 49 36 9 9 × 4 36 18 18 × 2 36 12 12 × 3 36
×
14 20 27 33 7 5 3 11 3 1, 3, 1, 3
Observe that, < < < . ∴ < < < 1, 1, 1, 1
36 36 36 36 18 9 4 12
Solved Examples
2 4 5 6 8 12
Ex 1. Show , ,,,, and 6 on the number line. Put the appropriate signs between the fractions given
6 6 6 6 6
below.
5 2 3 1 6 8 5
(a) (b) 0 (c) (d)
6 6 6 6 6 6 6
0 1 2
Sol.
0 1 2 3 4 5 6 8 12
6 6 6 6 6 6 6 6 6
(a) 5 > 2 (b) 3 > 0 (c) 1 < 6 (d) 8 > 5
6 6 6 6 6 6 6
Ex 2. Compare the following fractions and put the appropriate sign in the boxes.
3 5 1 1
(a) (b)
6 6 7 4
3 5
Sol. (a) < ( Like fractions and 3 < 5)
6 6
1 1
(b) < ( Unlike fractions with the same numerator and 4 < 7)
7 4 2
Ex 3. Rama read 25 pages of a book containing 100 pages while Sita read of the same book. Who read
fewer pages? 5
2 2
2
Sol. Number of pages read by Sita = of 100 = × 100 = × 20 = 40
5 5
Number of pages read by Rama = 25
Hence, Rama read fewer pages.
1 7
Ex 4. Jaidev takes 2 minutes to walk across the school ground. Rahul takes 4 minutes to do the same.
5
Who takes less time?
1 11 7
Sol. Jaidev takes 2 minutes = minutes. Rahul takes minutes.
5 5 4
×
×
11 11 4 44 7 75 35
Now, = = and = = [ LCM (5, 4) = 20]
×
×
5 54 20 4 45 20
11 7
44 > 35, so > .
5 4
So, Rahul takes less time.
204 Mathematics-6